Device Modeling of the Performance of Cu ( In , Ga ) Se 2 Solar Cells with V-Shaped Bandgap Profiles

1 Department of Electronic Engineering, Chang Gung University, 259 Wen-Hwa 1st Road, Kwei-Shan, Taoyuan 333, Taiwan 2Department of Photonics and Institute of Electro-Optical Engineering, National Chiao-Tung University, 1001 Ta Hsueh Road, Hsinchu 30013, Taiwan 3Department of Photonics Engineering, Yuan-Ze University, 135 Yuan-Tung Road, Chung-Li 32003, Taiwan 4Advanced Optoelectronic Technology Center, National Cheng Kung University, No. 1 University Road, Tainan 701, Taiwan


Introduction
Nowadays, it is an important issue to improve the conversion efficiency of thin-film solar cells.Impressively, the record conversion efficiency of thin-film Cu(In,Ga)Se 2 -based solar cells are to date over 20% [1].The major advantage of the CIGS-based solar cell is that the quaternary material system can attain a variable bandgap energy and lattice parameters by varying the Ga/(In+Ga) ratio [2].Chalcopyrite CIGS is reported to have an adjustable bandgap from 1.01 eV (CIS) to 1.636 eV (CGS) by changing the gallium content from 0 to 1 [3].However, only the position of the conduction-band edge will be affected when changing the CIGS bandgap [4,5].The latest reported high efficiency CIGS solar cell uses three-or multistage evaporation processes to prepare CIGS absorber layer with a double-graded bandgap profile, a higher gallium content towards the back and the front of the CIGS absorber layer, and a notch of low gallium content in between [6].From the other earlier research, the influence of the decreasing of gallium content from the buffer layer towards the notch of the absorber can enhance the electrons generated within the space-charge region [7].Furthermore, the potential benefit of the Ga content increases from notch towards the back contact induces a back-surface field in the conduction band, which causes electrons to drift away from the rear contact and thereby reduces the recombination at the back contact [8].As mentioned above, it is an excellent method to provide a variable bandgap of CIGS and obtain higher open circuit voltage and efficiency by using gallium to replace partial of indium.
However, it is hard to understand the benefits and effects of "grading" by studying the actual devices.Therefore, in order to understand how "grading" can improve cell performance, a novel approach is to use numerical modeling [9,10].In this paper, we investigate the influence of the Ga content numerically in the CIGS solar cells by modeling and device simulation.The amount of Ga doping is fixed in order to avoid the influence of open-circuit voltage by different

Simulation
The device characteristics of the CIGS solar cells are studied numerically using the APSYS simulation program, which was developed by Crosslight Software Inc. [11].The APSYS simulation program can deal with electrical properties by solving several interwoven equations including the basic Poisson's equation, drift-diffusion equations, photon rate equation, and scalar wave equation.To investigate the effect of bandgap grading in a CIGS solar cell, physical parameters of CIGS solar cells needed for electrical modeling are obtained from measurements and earlier literatures to construct the accurate model [12][13][14].Table 1 lists the parameters used in the numerical model.In the simulation, the model consists of several layers including 500-nm-thick AZO transparent conductive oxide layer, 50-nm-thick intrinsic ZnO layer, 50nm-thick CdS buffer layer, and 2-m-thick CIGS absorber layer.All simulations have been performed under an AM 1.5G light spectrum.
From the previous reports, the bandgap grading is dependent on the Ga composition, and the variation of the Ga/(In+Ga) ratio, , will affect the value of bandgap.The relation between Ga/(In+Ga) ratio and bandgap can be described by the following formula: where Eg CIS = 1.01 eV, Eg CGS = 1.636 eV,  = 0.167 eV, and the modeling reference of Ga grading profile was obtained from secondary ion mass spectroscopy (SIMS) data [15,16].
In order to confirm the validity of our model, the results of numerical analysis are compared with device measurement.Afterward two different types of absorber layer are discussed in detail.In the first type, we fix the Ga doping and vary bandgap notch depth (minimum bandgap).Whereas, the second type keeps bandgap notch depth unchanged but with different front grading (linear variation from notch increase towards the front side).After that, the electrical properties such as current density-voltage (J-V) curves, electric field intensity, and recombination intensity are investigated.

Results and Discussion
The cell structure and cross-sectional scanning electron microscopy (SEM) photographs of typical CIGS/Mo structure fabricated on Mo-coated soda-lime glass substrate are shown in Figure 1(a).SEM images show a reduction in grain size with increasing Ga content from top to bottom of absorber layer, which agrees well with the results by other groups [17].In Figure 1(b), the J-V curve from simulation is compared with experimental data, and inset shows the bandgap grading (Ga content) in absorber layer.From SIMS measurement result, one can find that bandgap shows a "V"shaped grading (see inset in Figure 1(b)) with the minimum gap locating at 150 nm from the CdS/CIGS surface (located at  = 0nm).All measurements and simulations are set under room temperature.At the same time, the simulation of J-V curve with V-shaped grading is corresponding well to measurements.This result indicates that the baseline parameters used in the model are in line with the physical properties of actual device.
It has been well known that Ga doping will not only change the CIGS bandgap but also obtain different open circuit voltage.The parameters are shown in Table 2. Therefore, in the simulation, we compare the samples with same amount of Ga contents in the absorber layer but different minimum bandgap in a distance of 150 nm from the CdS/CIGS surface as shown in inset of Figure 2(a).In addition, we also take the case with no V-shaped grading into consideration.The inset of Figure 1(b) shows the difference between the bandgap minimum and maximum close to the back contact and CdS buffer layer, which is defined as ΔEg Back and ΔEg Front , respectively.From Figure 2(a), the fill factor of photovoltaic device will increase as the depth of valley (minimum gap) in the absorber layer increases.As expected, more recombination might happen in the valley when the valley became deeper.Simultaneously, a stronger electric field is created to provide the carriers more energy to drift out the space charge region (SCR) as the ΔEg Back becomes larger as shown in Figure 2(b).In this way, the carrier collection will be increased and also the fill factor.From these results we can speculate that the positive ΔEg BF (ΔEg BF = ΔEg Back − ΔEg Front ) can reduce the recombination in the valley of absorber layer.
The effect of a ΔEg Front has been studied by many groups.Dullweber et al. [18] have observed that the slight increasing of Ga content in the front of the absorbers can not only enhance the electrons generated but also reduce SCR recombination.However, the Ga content increased strongly in the front of the absorber layer will cause a barrier for electrons.In Figure 3, the recombination intensity corresponding to five kinds of bandgap with different V-shaped grading has been investigated, the inset (a) and (b) show different type profile of the bandgap shape with different depth of bandgap minimum and ΔEg Front , respectively.Due to the fact that the   thermal energy in room temperature will cause the electrons to overcome it [19], the environmental temperature is set at 193 K in this simulation.
In the varied-notch depth cases, although the recombination intensity is stronger in the deeper notch situation, the ΔEg Back is also increased and provides a higher electric field for carriers to overcome the barrier, hence resulting in lower recombination intensity.In the ΔEg Front cases, larger slope will build up a higher barrier and cause the carriers to be localized in the valley to release energy via radiative recombination.In conclusion, there is an inversely proportional relation between the electric field intensity and recombination intensity.The higher electric field intensity and lower ΔEg Front will cause a lower recombination in the valley.In addition, as the ΔEg BF is positive, the recombination intensity is larger than that of the negative ΔEg BF , which agrees with our speculation.In order to illustrate the observed blocking behavior, the band diagrams of grading profiles are shown in Figure 4.
In Figure 4, the diagram describes the influence of ΔEg BF clearly.In the Figure 4(a), the ΔEg Back is larger than ΔEg Front (positive ΔEg BF ); ΔEg Back can produce an inner electric field to repel photo-induced electrons reach the backside, thereby reducing the back-surface recombination velocity.However, as Figure 4(b), the ΔEg Front is larger than ΔEg Back (negative ΔEg BF ); the inner electric field cannot give enough energy to electrons to reach CdS n-type layer.Therefore, the valley in the conduction band will trap the electrons and lead to an enhanced recombination velocity with the holes in the valence band which reduces the extraction of electricity.

Conclusion
In summary, we have developed a well-established model to study the CIGS solar cells with various bandgap absorber layers, and the results are corresponding well to actual device measurements.The simulation results show that a positive ΔEg BF can bring out an inner electric field to reduce back-surface recombination velocity and overcome the front barrier built up by ΔEg Front .On the contrary, the negative ΔEg BF will generate a barrier between CdS and CIGS layer, and the minority carriers (electrons) will be trapped in the valley easier and lead to low device conversion efficiency.In the future, this model can be adopted to optimize the bandgap grading type and fabricate high conversion efficiency CIGSbased thin film solar cell.

Figure 1 :
Figure 1: (a) Cell structure and cross-sectional SEM photographs of a CIGS/Mo solar cell fabricated on Mo-coated soda-lime glass substrate.(b) Simulation result from device modeling with baseline parameters including a grading bandgap compared with experimental J-V curve and SIMS data.

Figure 2 :Figure 3 :
Figure 2: (a) Current density-voltage curves and (b) electric filed intensity of CIGS cells with different bandgap grading profiles taken under illumination with an intensity of 1 sun at room temperature (300 K).

Figure 4 :
Figure 4: The band diagrams of CIGS solar cells with the cases (a) positive ΔEg BF and (b) negative ΔEg BF .

Table 1 :
Base parameters for CIGS numerical model.

Table 2 :
Photovoltaic parameters of different sample of CIGS solar cells.